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Block #181,853

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2013, 8:47:32 PM Β· Difficulty 9.8601 Β· 6,628,063 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
a551ae25d900671740d1dd782cbdfbb7598c9adf7a9cca1d75735725ca2b9e5c
View on Chainz β†—

Height

#181,853

Difficulty

9.860108

Transactions

1

Size

199 B

Version

2

Bits

09dc300f

Nonce

238,706

Timestamp

9/26/2013, 8:47:32 PM

Confirmations

6,628,063

Mined by

⛏️ P2SHAJgHpa8bWXAnCbvBMmWEijC8R51N2Bhnd4

Merkle Root

c5c713cec50db0decb5ad3ae0d8c0e97492c97c4345d834e6985c9519d842f8c
Transactions (1)
Coinbasec5c713cec50db0…85c9519d842f8c
1 in β†’ 1 out10.2700 XPM109 B
AJgHpa8b…1N2Bhnd4
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.423 Γ— 10⁹⁡(96-digit number)
14232527244644639790…86047877256523419229
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.423 Γ— 10⁹⁡(96-digit number)
14232527244644639790…86047877256523419229
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.846 Γ— 10⁹⁡(96-digit number)
28465054489289279581…72095754513046838459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.693 Γ— 10⁹⁡(96-digit number)
56930108978578559162…44191509026093676919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁢(97-digit number)
11386021795715711832…88383018052187353839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.277 Γ— 10⁹⁢(97-digit number)
22772043591431423664…76766036104374707679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.554 Γ— 10⁹⁢(97-digit number)
45544087182862847329…53532072208749415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.108 Γ— 10⁹⁢(97-digit number)
91088174365725694659…07064144417498830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.821 Γ— 10⁹⁷(98-digit number)
18217634873145138931…14128288834997661439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.643 Γ— 10⁹⁷(98-digit number)
36435269746290277863…28256577669995322879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,723,412 XPMΒ·at block #6,809,915 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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